Questions tagged [category-theory]

Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. (By Steve Awodey)

Functors in category theory, and also in its application to functional programming, can be seen as a kind of "structured" functions: Given two sets $A,B$, rather than just having a function $f:A\to B$,...

I was studying the definition of currying and uncurrying using Category Theory from these slides. The answer and the proof on slide 19 makes 100% sense to me however, the definitions seem to come out ...

I'm reading the paper "Dual of substitution is Redecoration".
And I'm struggling with understanding the usage of the word "not-well-founded cotrees".
what is a cotree compared to a tree ? I suspect ...

Wondering if there are any documents, theories, or methodologies for dealing with mutable memory mathematically. Basically a formal algebraic model of how computers manipulate memory. Along the lines ...

Here I am talking about the Functor category, which is defined as a category whose objects are functors and morphisms are natural transformations.
For reference: https://ncatlab.org/nlab/show/functor+...

After reading about Category Theory at https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ I was wondering whether we can represent any program by means of a walk of a ...

I'm looking for some pointers on proper mathematical (FP?, category-theory?) terminology.
My apologies if the below is somewhat imprecise; I suppose the precision is precisely what I'm looking for in ...

There is a great divide in Haskell between pure and monadic algorithms. While the latter are indistinguishable from their usual imperative counterparts, the former can get much more magical. What this ...

I am not a computer scientist and have no knowledge of programming.
However, I wondered continuations occur as natural and interesting mathematical structures, perhaps as algebraic or type theoretic ...

Suppose we have a System F term $f : \forall \alpha. \alpha\times\alpha\to\alpha$, interpreted in a parametric model which is a bicartesian closed category.
I was wondering if in such context it is ...

It comes from big data perspective. Basically, many frameworks (like Apache Spark) "compensate" lack of relational operations by providing Functor/Monad-like interfaces and there is a similar movement ...

So I'm almost done teaching myself category theory. One of the main take-aways for me is that type constructors (higher-kinded types) are endo-functors.
But it this always the case? What's throwing ...

I keep hearing about how one must learn category theory to truly understand programming language theory. So far, I've learned a good deal of PL without ever stepping foot into the realm of categories. ...

I'm currently developing a simple key-value NoSQL store and want to build its formal model. I found article about key value formalisation with category theory, but I'm interested are there some works ...

In the model of (functional) programming languages as a category where the objects are types and the arrows are functions, I'm trying to really understand what's really the identity arrow.
Barr-Wells ...

Could most categories , or a finite part of them be represented on a subset of a complete graph of N vertices (Kn) which is connected. and partly directed? Could all the axioms of category theory be ...

I read that Category Theory has alot to do with how programs and information can be organised.Can Category theory simplify various programming strategies? If a specific Category is represented as a ...

I see how objects in a category stand for types, but where do I find the terms and more specifically the rules which tell me which of them are allowed? When I e.g. consider a Cartesian closed category ...